Exam 5: Trigonometric Functions

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 7 , - 6 ) ;$ Find $\cot \theta$ .

(Multiple Choice)

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Question 281

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { 1 } { 2 }$

(Multiple Choice)

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Question 282

Find the exact value of the expression. - $\cos 210 ^ { \circ }$

(Multiple Choice)

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Question 283

Solve the problem. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

(Multiple Choice)

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Question 284

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\tan 60 ^ { \circ }$

(Multiple Choice)

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Question 285

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sin 27 ^ { \circ }$

(Multiple Choice)

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Question 286

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $170 ^ { \circ }$

(Multiple Choice)

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Question 287

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 15,20 )$ ; Find $\csc \theta$ .

(Multiple Choice)

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Question 288

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cot 45 ^ { \circ }$

(Multiple Choice)

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Question 289

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 122 ^ { \circ }$

(Multiple Choice)

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Question 290

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $44 ^ { \circ } 40 ^ { \prime }$ . If Joey is known to be standing 14 feet from the base of the tree, how tall is the tree (to the nearest foot)?

(Multiple Choice)

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Question 291

Find the reference angle for the given angle. - $207.3 ^ { \circ }$

(Multiple Choice)

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Question 292

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\cot \theta = 1.8857855$

(Multiple Choice)

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Question 293

Provide an appropriate response. -Find the complement of an angle whose measure is 39°17′.

(Multiple Choice)

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Question 294

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\tan 62 ^ { \circ } 52 ^ { \prime }$

(Multiple Choice)

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Question 295

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $295 ^ { \circ }$

(Multiple Choice)

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Question 296

Solve the problem. -Find the exact value of $x$ in the figure.

(Multiple Choice)

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Question 297

Solve the problem. -A contractor needs to know the height of a building to estimate the cost of a job. From a point 99 feet away from the base of the building, the angle of elevation to the top of the building is found to be $42 ^ { \circ } 59 ^ { \prime }$ . Find the height of the building. Round your answer to the hundredths place when necessary.

(Multiple Choice)

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Question 298

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

(Multiple Choice)

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Question 299

Find the exact value of the expression. - $\csc 240 ^ { \circ }$

(Multiple Choice)

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Question 300

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 7 , - 6 ) ;$ Find $\cot \theta$ .

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { 1 } { 2 }$

Find the exact value of the expression. - $\cos 210 ^ { \circ }$

Solve the problem. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\tan 60 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sin 27 ^ { \circ }$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $170 ^ { \circ }$

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 15,20 )$ ; Find $\csc \theta$ .

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cot 45 ^ { \circ }$

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 122 ^ { \circ }$

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $44 ^ { \circ } 40 ^ { \prime }$ . If Joey is known to be standing 14 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Find the reference angle for the given angle. - $207.3 ^ { \circ }$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\cot \theta = 1.8857855$

Provide an appropriate response. -Find the complement of an angle whose measure is 39°17′.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\tan 62 ^ { \circ } 52 ^ { \prime }$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $295 ^ { \circ }$

Solve the problem. -Find the exact value of $x$ in the figure.

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Find the exact value of the expression. - $\csc 240 ^ { \circ }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

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Exam 5: Trigonometric Functions

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - (7,−6);( 7 , - 6 ) ;(7,−6); Find cot⁡θ\cot \thetacotθ .

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - sin⁡θ=−12\sin \theta = - \frac { 1 } { 2 }sinθ=−21​

Find the exact value of the expression. - cos⁡210∘\cos 210 ^ { \circ }cos210∘

Solve the problem. -On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 50 meters long and the tree is 40 meters tall, how long is the shadow?

Without using a calculator, give the exact trigonometric function value with rational denominator. - tan⁡60∘\tan 60 ^ { \circ }tan60∘

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - sin⁡27∘\sin 27 ^ { \circ }sin27∘

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - 170∘170 ^ { \circ }170∘

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - (15,20)( 15,20 )(15,20) ; Find csc⁡θ\csc \thetacscθ .

Without using a calculator, give the exact trigonometric function value with rational denominator. - cot⁡45∘\cot 45 ^ { \circ }cot45∘

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - −122∘- 122 ^ { \circ }−122∘

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 44∘40′44 ^ { \circ } 40 ^ { \prime }44∘40′ . If Joey is known to be standing 14 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Find the reference angle for the given angle. - 207.3∘207.3 ^ { \circ }207.3∘

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - cot⁡θ=1.8857855\cot \theta = 1.8857855cotθ=1.8857855

Provide an appropriate response. -Find the complement of an angle whose measure is 39°17′.

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - tan⁡62∘52′\tan 62 ^ { \circ } 52 ^ { \prime }tan62∘52′

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - 295∘295 ^ { \circ }295∘

Solve the problem. -Find the exact value of xxx in the figure.

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant III and the positive xxx -axis is 12\frac { 1 } { 2 }21​ .

Find the exact value of the expression. - csc⁡240∘\csc 240 ^ { \circ }csc240∘

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 7 , - 6 ) ;$ Find $\cot \theta$ .

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\sin \theta = - \frac { 1 } { 2 }$

Find the exact value of the expression. - $\cos 210 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\tan 60 ^ { \circ }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sin 27 ^ { \circ }$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $170 ^ { \circ }$

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ. - $( 15,20 )$ ; Find $\csc \theta$ .

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\cot 45 ^ { \circ }$

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $- 122 ^ { \circ }$

Solve the problem. -When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is $44 ^ { \circ } 40 ^ { \prime }$ . If Joey is known to be standing 14 feet from the base of the tree, how tall is the tree (to the nearest foot)?

Find the reference angle for the given angle. - $207.3 ^ { \circ }$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\cot \theta = 1.8857855$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\tan 62 ^ { \circ } 52 ^ { \prime }$

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. - $295 ^ { \circ }$

Solve the problem. -Find the exact value of $x$ in the figure.

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Find the exact value of the expression. - $\csc 240 ^ { \circ }$